A capillary tube of radius $r$ can support a liquid column of height $h$. If the tube is cut at a he

Question

A capillary tube of radius $r$ can support a liquid column of height $h$. If the tube is cut at a height $h/2$ and the original angle of contact was $0^{\circ}$, the new radius of curvature of the meniscus at the top of the cut tube will be

Professor PC Thomas Classes · Answer

(b) : When a capillary tube is of insufficient length, the liquid does not overflow. Instead, it rises to the top edge and its meniscus flattens out, changing its radius of curvature $R$ such that $h R = 	ext{constant}$. Let the new height be $h'$ and the new radius of curvature be $R'$. We have $h R = h' R'$. The original radius of curvature $R = \frac{r}{\cos 0^{\circ}} = r$. Thus, $h 	imes r = (h/2) 	imes R'$. Solving for $R'$ gives $R' = 2r$.